Title: The Suboptimal Proposal.
Abstract: The Particle Filter is a classical method to combine information from a (chaotic, nonlinear, stochastic) model with data. Notions of the certainty or uncertainty in measurements, of the correlations between predictions in different locations in model/data space, and of the certainty of the final estimate are all naturally incorporated in the particle filtering framework. Furthermore the particle filter estimate of the state is known to converge to the best possible estimate as the computational cost, or the number of particles, approaches infinity, for arbitrary problems. Nonetheless the Particle Filter exhibits an undesirable degeneracy when applied to estimate a high-dimensional state, requiring an infeasible number of particles. I will introduce an algorithm called the "Suboptimal Proposal" that is not a Particle Filter, but instead converges to one. The Suboptimal Proposal fits into an ongoing series of attempts to mix the Particle and Ensemble Kalman Filters. I will show that this algorithm improves on past attempts in resolving high-dimensional, strongly nonlinear systems, but ultimately argue that it provides another nail in the coffin of the search for a perfectly flexible mixture of the two filters.